Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Gottlob Frege and Michael Potter
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15 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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13455
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Frege did not think of himself as working with sets [Frege, by Hart,WD]
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10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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9157
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The null set is only defensible if it is the extension of an empty concept [Frege, by Burge]
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9835
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It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
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16895
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The null set is indefensible, because it collects nothing [Frege, by Burge]
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14238
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A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
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10713
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Usually the only reason given for accepting the empty set is convenience [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
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9854
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We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett]
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9883
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Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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18104
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Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock]
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13044
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Infinity: There is at least one limit level [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
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9834
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A class is, for Frege, the extension of a concept [Frege, by Dummett]
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3328
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Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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10708
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Nowadays we derive our conception of collections from the dependence between them [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13546
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
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